$f(α)$ Multifractal spectrum at strong and weak disorder

Abstract

The system size dependence of the multifractal spectrum $f(α)$ and its singularity strength $α$ is investigated numerically. We focus on one-dimensional (1D) and 2D disordered systems with long-range random hopping amplitudes in both the strong and the weak disorder regime. At the macroscopic limit, it is shown that $f(α)$ is parabolic in the weak disorder regime. In the case of strong disorder, on the other hand, $f(α)$ strongly deviates from parabolicity. Within our numerical uncertainties it has been found that all corrections to the parabolic form vanish at some finite value of the coupling strength.